Question

Let f (x) = x|x| and g(x) = sin x.
Statement-1 : gof is differentiable at x = 0 and its derivative is continuous at that point.

Statement-2 : gof is twice differentiable at x = 0.

(a) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1  
(b) Statement- 1 is true, Statement-2 is false  
(c) Statement-1 is false, Statement-2 is true  
(d) Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

Answer 1

Let the composite function gof (x) be denoted by H(x).

LH′′(0) = –2 and RH′′(0) = 2
Thus H(x) is NOT twice differentiable at x = 0​